I do not know how complementarity is applied to this scenario - anyone
else have a suggestion?

On Sat, Aug 14, 2004 at 04:56:12PM -0700, Fred Chen wrote:
> Russell, I agree with what you state below. But consider the following
> experiment.
> 
> Instead of two beams of equal intensity interfering, as in classical
> inteferometry, one has unequal amplitude beams. Specifically,
> 
> Beam A: 0.9*exp(iax+ibz-iwt)
> Beam B: 0.1*exp(-iax+ibz-iwt)
> 
> The interference pattern is of the form:
> 
> Interference field = [cos(ax)+i*0.8sin(ax)]exp(ibx-iwt)
> 
> So the resulting photon distribution follows the intensity, or the field
> amplitude squared:
> 
> Interference intensity = 0.64+ 0.36*cos^2(ax)
> 
> This wave pattern will begin to appear after sufficient number of
> photons, but each photon is always ~99% (81/82) likely to have
> originated from Beam A, based on conservation.
> 
> If Beam A and Beam B had different amplitudes, you would maximize the
> uncertainty of the photon origin since you have to say 50/50 likelihood
> for a photon coming from either A or B. 
> 
> The complementarity principle's strongest statement is 100% certainty,
> and that cannot be attained. But we can still get an idea of the wave
> interference pattern and 'which way' information with high (but not
> 100%) certainty in gray-transition cases such as above.
> 
> Fred
> 
> -----Original Message-----
> From: Russell Standish [mailto:[EMAIL PROTECTED] 
> Sent: Saturday, August 14, 2004 2:51 AM
> To: Fred Chen
> Cc: 'Everything List'
> Subject: Re: Quantum Rebel
> 
> 
> On Fri, Aug 13, 2004 at 11:43:10PM -0700, Fred Chen wrote:
> ...
> 
> > 
> > A better (and far simpler) way to challenge complementarity would be 
> > to use a low-intensity interferogram in a photographic film or CCD. At
> 
> > first the photons being detected are few so the shot (particle-like) 
> > aspect is more obvious. As more photons are integrated, the classical 
> > interference pattern is observed. Can there be a transition region 
> > where both aspects are observable?
> > 
> 
> This does not challenge complementarity. Consider a double slit
> apparatus with the photon source's intensity down so low that each
> individual photon can be observed hitting the screen one at a time. But
> when one plots the distribution of positions where the photons strike
> the screen after observing many of them, the interference pattern
> results. This is simple and uncomplicated, but is not what the
> complementarity principle is about.
> 
> Now consider that you have information about which slit the photon
> passed through before hitting the screen - ie each photon is labelled 1,
> 2, 1, 1, etc, according to whuch slit it passed through. Therefore, you
> can separate the observed photons into two sets, according to which slit
> the phtons passed through. The distribution of each subset corresponds
> to a single slit experiment, and the final distribution must be the sum
> of the two single slit experiements. But single slit experiments do not
> have interference patterns - hence the sum cannot have an interference
> pattern either.
> 
> Consequently, if you have any way of knowing which slit the photon went
> through (the "which way" information), then you cannot have an
> interference pattern. This is what the complementarity principle means.
> 
>                                       Cheers
> -- 
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> ------------------------------------------------------------------------
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A/Prof Russell Standish                  Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052                         Fax   9385 6965, 0425 253119 (")
Australia                                [EMAIL PROTECTED]             
Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02
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